Instant runoff voting (IRV) has recently gained popularity as an alternative to plurality voting for political elections, with advocates claiming a range of advantages, including that it produces more moderate winners than plurality and could thus help address polarization. However, there is little theoretical backing for this claim, with existing evidence focused on case studies and simulations. In this work, we prove that IRV has a moderating effect relative to plurality voting in a precise sense, developed in a 1-dimensional Euclidean model of voter preferences. Our results show that as long as voters are symmetrically distributed and not too concentrated at the extremes, IRV cannot elect an extreme candidate over a moderate. In contrast, we show plurality can. Our methods develop new frameworks for the theoretical analysis of voting systems, deriving exact winner distributions geometrically and establishing a connection between plurality voting and stick-breaking processes.

翻译：即时决选投票（IRV）近年来作为复数投票在政治选举中的替代方案日益普及，支持者声称其具有诸多优势，包括比复数投票更能产生温和的胜选者，从而有助于缓解两极分化。然而，这一主张缺乏理论支撑，现有证据主要集中于案例研究与模拟分析。本研究在精确意义上证明，在选民偏好的一维欧几里得模型中，IRV相对于复数投票具有调节效应。结果表明：只要选民分布对称且未过度集中于极端区间，IRV便无法使极端候选人击败温和候选人。相比之下，复数投票则可能产生此类结果。我们开发了投票系统理论分析的新框架，通过几何方法推导出精确的胜选者分布，并建立了复数投票与棍棒断裂过程之间的关联。